Electronic Theses and Dissertations

Date

2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Committee Chair

Ebenezer George

Committee Member

Andrews Anum

Committee Member

Deo Kumar Srivastava

Committee Member

Majid Noroozi

Abstract

Epidemiology has become increasingly concerned with measurements subject to detection limits, by which, values below this limit become left-censored. Traditional methods for handling such approaches have been found to be effective, provided necessary assumptions and conditions are met for the methods to work appropriately. However, when such conditions fail to be met or assumptions are incorrect, the effect this has on the method’s performance becomes serious. One such method is multiple imputation, which relies on assuming the distribution of the measurements when imputing quantities below the level of detection. As the reliance on the assumption can prove very strong in the performance of handling below level of detection data, recommendation has been given to investigating methodologies that can best analyze left-censored data while limiting the number of assumptions made about the underlying structure of that data. Such methods were recommended by prominent figures in left-censored literature and similar approaches with limited assumptions about the data structure have found good performance on below level of detection data. Bayesian approaches become a prime candidate by utilizing noninformative prior distributions that emphasize the data over assumed beliefs, these priors are updated using the data to valid posterior distributions whose parameters are influenced by the derived distributions. This provides strong advantages for Bayesian approaches that other common methods are unable to easily replicate with methodologies that either impute through uniform mechanisms or require sampling from assumed distributions. These offer strong advancements with Bayesian methods when implemented on data below the level of detection where assumptions prove more difficult. Despite this, modern literature tends to assume some structural qualities about the data and little has been investigated in the behavior of Bayesian procedures when the specifications of structure are entirely noninformative. In this dissertation, we develop a simulation study to examine the performance of a Bayesian method for multiple imputation towards left-censored data in a case-control study framework using entirely noninformative specifications of the data and linear model assumptions. The approach begins by reviewing the performance on uncorrelated response variables before looking at more complicated relationships, such as when the responses are correlated and the correlation is unknown.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest.

Notes

Open Access

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